Robert Heinlein's Farmer in the Sky mentions microwave ovens and his Red Planet Mars opens with a cell phone call. Both are early Fifties.
Well, those are both technologies whose seeds were planted in WWII. It was WWII radar operators who first noticed that things got hot when placed in the path of a strong radar (microwave) beam. And mobile telephones have actually been around in nascent form since the late '40s, though the early models were car-mounted. (And let's keep in mind that there's a difference between a mobile phone and a cellular phone. "Cell/cellular" refers to the particular type of network that modern mobile phones use. If there was a mobile phone in Red Planet
-- presumably the book you meant to refer to -- I doubt RAH specified it was cellular.)
But the cell phone thing was anticipated in a way by Chester Ward (if I remember the name correctly) in the Dick Tracy comic strip.
Chester Gould. Dick Tracy wore a "2-way wrist radio," which could be considered more of a compact walkie-talkie or portable equivalent of a squad car radio than a telephone per se, but it was ahead of its time. And by the '60s it had been upgraded to a 2-way wrist television (though "wrist" was something of a misnomer, since it had an antenna wire that ran all the way along Tracy's sleeve under his jacket, as seen in the first panel here
I've never found the cellular phone phenomenon to be as dramatic a technological revelation as some other technologies, since after all, mobile communications have been available for a long time, its just the sophistication that has changed. Smartphones are a little different, by adding a lot of features (gps, im, txt, ereaders, weather, www) they have made the information age more mobile.
Star Trek communicators are also different, while ostensibly the precursors to modern flip phones, they actually would have to be a lot more sophisticated, since they work over subspace.